Answer
The graph is shown below.
Work Step by Step
The inequality is
$y\leq2x-1$
Step 1:- Replace the inequality symbol with $=$ and graph the linear equation.
$y=2x-1$
Now use the slope and the $y-$ intercept to graph.
The equation is in the form of $y=mx+b$.
Where, slope $m=\frac{2}{1}=\frac{Rise}{Run}$ and $y-$ intercept $=-1$.
Therefore the first point is $A=(0,-1)$
For the second point we move two units up (rise) and one units right side (run).
The second point is $B=(1,1)$
There is equality sign therefore we draw a solid line through both points.
Step 2:- Choose a test point and plug into the inequality.
Let the test point $C=(1,0)$.
Plug the test point into inequality.
$\Rightarrow (0)\leq2(1)-1$
Simplify.
$\Rightarrow 0\leq2-1$
$\Rightarrow 0\leq1$
The statement is correct.
The solution set contains the test point.
Hence, the lower part of the line is the solution set.
